Hyperbolic Function Calculator
Evaluate Hyperbolic Functions
Calculate all hyperbolic functions for a given value
Inverse Hyperbolic Functions
Calculate arcsinh, arccosh, arctanh
Formula
sinh(x) = (eˣ-e⁻ˣ)/2 | cosh(x) = (eˣ+e⁻ˣ)/2 | cosh²-sinh² = 1 | arcsinh(x) = ln(x+√(x²+1))
Frequently Asked Questions
What are hyperbolic functions?
Hyperbolic functions are analogs of trig functions defined using exponentials: sinh(x) = (eˣ - e⁻ˣ)/2, cosh(x) = (eˣ + e⁻ˣ)/2, tanh(x) = sinh(x)/cosh(x). They describe the shape of hanging cables (catenaries) and appear in relativity and engineering.
How are hyperbolic functions related to exponentials?
sinh(x) = (eˣ - e⁻ˣ)/2 and cosh(x) = (eˣ + e⁻ˣ)/2. The key identity is cosh²(x) - sinh²(x) = 1 (compared to sin²+cos² = 1 for trig). Inverse hyperbolics can be expressed as logarithms: arcsinh(x) = ln(x + √(x²+1)).
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